Artists have used assemblies of 3D planar sections for more than a century to express both realistic forms and abstract ideas. Evidence suggests that symbolic abstractions dominate a mental model of objects. Thus, across cultures, users both recognize shape proxies quickly and tend to communicate objects by drawing them as symbolic abstractions. Artists and sculptors have long explored minimalist shape proxies, including planar section representations, to highlight defining aspects of familiar objects, and examples of such representations may be found throughout the world.
Planar sections of 3D shapes, due to their ease of assembly from compactly manufactured and packed 2D sheets, are an exemplary platform to study the junction of design, manufacturing, and human perception. Conceptually, there are two sources from which a planar abstraction might be created. The first source is pre-existing geometry. The second source, an artist or designer's creative intent, remains mainly unaddressed in prior disclosures.
Mathematically, a planar section representation is a non-empty set of planar sections. A planar section is defined geometrically by a unique 3D-embedded plane and one or more closed boundary curves that lie on the plane. No curve self-intersects and there are no intersections between any two coplanar curves.
The creation of planar sections by slicing existing 3D objects has received much attention in both research and industry. Problematically, planar section contours do not often lie precisely on 3D models. Additionally, fluid interfaces for sketching such planar section assemblies from scratch or combined with slices of existing 3D objects are relatively unexplored. Interfaces for creating such assemblies have application outside their direct outcome of 3D planar section sculptures, as these planar structures can form scaffolds for digital modelling and armatures for instrumented animatronics.
With laser cutting machines and 3D printers becoming increasingly accessible, it is expected that a wider audience will seek to create their own objects and general research in the areas of interactive systems and geometric algorithms to aid object design in the field of computer graphics remains active. Thus, automation of complex operations is desirable.